Mathematical (Arithmetic) representation of XOR

Question

I have spent the last 5 hours searching for an answer. Even though I have found many answers they have not helped in any way.

What I am basically looking for is a mathem

Answer 1

"mathematical, arithmetic only representation" are not correct terms anyway. What you are looking for is a function which goes from IxI to I (domain of integer numbers).
Which restrictions would you like to have on this function? Only linear algebra? (+ , - , * , /) then it's impossible to emulate the XOR operator.
If instead you accept some non-linear operators like Max() Sgn() etc, you can emulate the XOR operator with some "simpler" operators.